Chapter 7.1, Problem 19E

a.

To determine

To find: The position of the particle at the end of the trip.

Answer to Problem 19E

The position of the particle at the end of the trip is $5\text{ m}$ .

Explanation of Solution

Given information:

The graph of the velocity of the particle is given.

Calculation:

The area under the curve from $t=0$ to $t=1$ is $-{\text{1 m}}^2$ , from $t=1$ to $t=5$ is ${\text{5 m}}^2$ , from $t=5$ to $t=7$ is $-{\text{1 m}}^2$ .

Therefore, $\text{Displacement}=-1+5-1=3$ .

Then,

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement}\\ =2+3\\ =5\text{ m}\end{array}$

Conclusion:

The position of the particle at the end of the trip is $5\text{ m}$ .

b.

To determine

To find: The total distance traveled by the particle.

Answer to Problem 19E

The total distance traveled by the particle is $7\text{ m}$ .

Explanation of Solution

Given information:

The graph of the velocity of the particle is given.

Calculation:

The area under the curve from $t=0$ to $t=1$ is $-{\text{1 m}}^2$ , from $t=1$ to $t=5$ is ${\text{5 m}}^2$ , from $t=5$ to $t=7$ is $-{\text{1 m}}^2$ .

The total distance traveled is $\left|-1\right|+\left|5\right|+\left|-1\right|=7\text{ m}$ .

Conclusion:

The total distance traveled by the particle is $7\text{ m}$ .